Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2014. / Cataloged from PDF version of thesis. / Includes bibliographical references (pages 99-101). / Let G be a connected reductive group with a split maximal torus defined over a nonarchimedean local field. I evaluate a matrix coefficient of the unramified principal series of G known as the "Bessel function" at torus elements of dominant coweight. I show that the Bessel function shares many properties with the Macdonald spherical function of G, in particular the properties described in Casselman's 1980 evaluation of that function. The analogy I demonstrate between the Bessel and Macdonald spherical functions extends to an analogy between the spherical Whittaker function, evaluated by Casselman and Shalika in 1980, and a previously unstudied matrix coefficient. / by Mario A. DeFranco. / Ph. D.
| Identifer | oai:union.ndltd.org:MIT/oai:dspace.mit.edu:1721.1/90183 |
| Date | January 2014 |
| Creators | DeFranco, Mario A. (Mario Anthony) |
| Contributors | Benjamin Brubaker., Massachusetts Institute of Technology. Department of Mathematics., Massachusetts Institute of Technology. Department of Mathematics. |
| Publisher | Massachusetts Institute of Technology |
| Source Sets | M.I.T. Theses and Dissertation |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | 101 pages, application/pdf |
| Rights | M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission., http://dspace.mit.edu/handle/1721.1/7582 |
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